Conference in Memory of Robert Osserman

A full day program centered around Bob's mathematical career and its influences in geometry.

Blaine Lawson, Stony Brook

Reflections on the early mathematical life of Bob Osserman

This talk will be a general exposition of some of Bob Osserman's seminal contributions to the theory of minimal surfaces. The presentation will be aimed at a wide mathematical audience, and early parts of the talk should be accessible to non-mathematicians as well.

The purpose of this talk is to review some results in classical minimal surface theory and to present a few mathematical problems on soap films, properly embedded minimal surfaces with finite topology and minimizing properties of periodic surfaces. These facts depend on relations between classic surface geometry, riemann surface theory, and geometric analysis.

As part of his work understanding higher curvatures, Bob encountered a little-known paper by the statistician Harold Hotelling on the volume of tubes. He asked me what statistics problems this relates to. His questions have led to an active development of a variety of extensions of weyl’s formulæ.